document.write( "Question 105122: Need help solving: 3x^2-2x+1=0 using the quadratic formula. I'm getting weird answer and it is confusing me. \n" ); document.write( "
Algebra.Com's Answer #76493 by MathLover1(20849)\"\" \"About 
You can put this solution on YOUR website!
\r
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:

\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( " Starting with the general quadratic
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"ax%5E2%2Bbx%2Bc=0\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " the general solution using the quadratic equation is:
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So lets solve \"3%2Ax%5E2-2%2Ax%2B1=0\" ( notice \"a=3\", \"b=-2\", and \"c=1\")
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%28--2+%2B-+sqrt%28+%28-2%29%5E2-4%2A3%2A1+%29%29%2F%282%2A3%29\" Plug in a=3, b=-2, and c=1
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%2A3%2A1+%29%29%2F%282%2A3%29\" Negate -2 to get 2
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%282+%2B-+sqrt%28+4-4%2A3%2A1+%29%29%2F%282%2A3%29\" Square -2 to get 4 (note: remember when you square -2, you must square the negative as well. This is because \"%28-2%29%5E2=-2%2A-2=4\".)
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%282+%2B-+sqrt%28+4%2B-12+%29%29%2F%282%2A3%29\" Multiply \"-4%2A1%2A3\" to get \"-12\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%282+%2B-+sqrt%28+-8+%29%29%2F%282%2A3%29\" Combine like terms in the radicand (everything under the square root)
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%282+%2B-+2%2Ai%2Asqrt%282%29%29%2F%282%2A3%29\" Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%282+%2B-+2%2Ai%2Asqrt%282%29%29%2F%286%29\" Multiply 2 and 3 to get 6
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " After simplifying, the quadratic has roots of
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x=1%2F3%2Bsqrt%282%29%2F3%2Ai\" or \"x=1%2F3-sqrt%282%29%2F3%2Ai\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "

\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );